No process measurement can be considered perfect. The instrumentation itself is subject to error and data collection is subject to inaccuracies in time‐stamping. It is for this reason that we never expect heat and mass balances to close perfectly. However performing such a balance is effectively a comparison between two ‘opinions’ of the true value – one measured directly and the other derived from the other measurements involved in the balance. Data reconciliation is a technique that uses these multiple estimates to produce an estimate that is more reliable than any of them.
Consider, as a simple example, that we have two measurements of the same property – both subject to error. The first has a standard deviation of σ1, the second σ2. The values of each of these measurements can be considered to have come from two distributions with different means, i.e. μ1 and μ2. Our aim is to choose the most likely estimate. This will be a weighted average of the two measurements, where a and (1 − a) are the weighting coefficients. This estimate will therefore have the mean
Provided the errors in the two measurements are not correlated then the standard deviation is
The best estimate will have the smallest standard deviation. This will occur when